Powers J.M. Lecture Notes on Fundamentals of Combustion

University of Notre Dame, Indiana, Department of Aerospace and Mechanical Engineering, USA, 2011. 409 p.

Contents.
Preface.
Introduction to kinetics.
Isothermal, isochoric kinetics O ? O2 dissociation.
Pair of irreversible reactions.
Mathematical model.
Example calculation.
Species concentration versus time.
Pressure versus time.
Dynamical system form.
E?ect of temperature.
Single reversible reaction.
Mathematical model.
Kinetics.
Thermodynamics.
Example calculation.
Zel’dovich mechanism of NO production.
Mathematical model.
Standard model form.
Reduced form.
Example calculation.
Stiffness, time scales, and numerics.
Effect of temperature.
Effect of initial pressure.
Stiffness and numerics.
Adiabatic, isochoric kinetics.
Thermal explosion theory.
One-step reversible kinetics.
First law of thermodynamics.
Dimensionless form.
Example calculation.
High activation energy asymptotics.
Detailed H2 ? O2 ? N2 kinetics.
Gas mixtures.
Some general issues.
Ideal and non-ideal mixtures.
Ideal mixtures of ideal gases.
Dalton model.
Binary mixtures.
Entropy of mixing.
Mixtures of constant mass fraction.
Summary of properties for the Dalton mixture model.
Amagat model*.
Mathematical foundations of thermodynamics*.
Exact diffrentials and state functions.
Two independent variables.
Legendre transformations.
Heat capacity.
Van der Waals gas.
Redlich-Kwong gas.
Compressibility and generalized charts.
Mixtures with variable composition.
Partial molar properties.
Homogeneous functions.
Gibbs free energy.
Other properties.
Relation between mixture and partial molar properties.
Frozen sound speed.
Irreversibility in a closed multicomponent system.
Equilibrium in a two-component system.
Phase equilibrium.
Chemical equilibrium: introduction.
Isothermal, isochoric system.
Isothermal, isobaric system.
Equilibrium condition.
Thermochemistry of a single reaction.
Molecular mass.
Stoichiometry.
General development.
Fuel-air mixtures.
First law analysis of reacting systems.
Enthalpy of formation.
Enthalpy and inteal energy of combustion.
Adiabatic ?ame temperature in isochoric stoichiometric systems.
Undiluted, cold mixture.
Dilute, cold mixture.
Dilute, preheated mixture.
Dilute, preheated mixture with minor species.
Chemical equilibrium.
Chemical kinetics of a single isothermal reaction.
Isochoric systems.
Isobaric systems.
Some conservation and evolution equations.
Total mass conservation: isochoric reaction.
Element mass conservation: isochoric reaction.
Energy conservation: adiabatic, isochoric reaction.
Energy conservation: adiabatic, isobaric reaction.
Non-adiabatic isochoric combustion.
Entropy evolution: Clausius-Duhem relation.
Simple one-step kinetics.
Thermochemistry of multiple reactions.
Summary of multiple reaction extensions.
Equilibrium conditions.
Minimization of G via Lagrange multipliers.
Equilibration of all reactions.
Zel’dovich’s uniqueness proof*.
Isothermal, isochoric case.
Isothermal, isobaric case.
Adiabatic, isochoric case.
Adiabatic, isobaric case.
Concise reaction rate law formulations.
Reaction dominant: J ? (N ? L).
Species dominant: J (N ? L).
Onsager reciprocity.
Irreversibility production rate.
Reactive Navier-Stokes equations.
Evolution axioms.
Conservative form.
Non-conservative form.
Mass.
Linear momentum.
Energy.
Second law.
Species.
Elements.
Mixture rules.
Constitutive models.
Temperature evolution.
Shvab-Zel’dovich formulation.
Simple solid combustion: Reaction-diffusion.
Simple planar model.
Model equations.
Simple planar derivation.
Ad hoc approximation.
Planar formulation.
More general coordinate systems.
Non-dimensionalization.
Dffusion time discussion.
Final form.
ntegral form.
n?nite Damk?ohler limit.
Steady solutions.
High activation energy asymptotics.
Method of weighted residuals.
One-term collocation solution.
Two-term collocation solution.
Steady solution with depletion.
Unsteady solutions.
Linear stability.
Formulation.
Separation of variables.
Numerical eigenvalue solution.
Low temperature transients.
ntermediate temperature transients.
High temperature transients.
Full transient solution.
Low temperature solution.
High temperature solution.
Laminar ?ames: Reaction-advection-di?usion.
Goveing Equations.
Evolution equations.
Conservative form.
Non-conservative form.
Formulation using enthalpy.
Low Mach number limit.
Constitutive models.
Alteate forms.
Species equation.
Energy equation.
Shvab-Zel’dovich form.
Equilibrium conditions.
Steady buer-stabilized ?ames.
Formulation.
Solution procedure.
Model linear system.
System of ?rst order equations.
Equilibrium.
Linear stability of equilibrium.
Laminar ?ame structure.
TIG =0.2.
TIG =0.076.
Detailed H2-O2-N2 kinetics.
Simple detonations: Reaction-advection.
Reactive Euler equations.
One-step irreversible kinetics.
Thermicity.
Parameters for H2-Air.
Conservative form.
Non-conservative form.
Mass.
Linear momenta.
Energy.
Reaction.
Summary.
One-dimensional form.
Conservative form.
Non-conservative form.
Reduction of energy equation.
Characteristic form.
Rankine-Hugoniot jump conditions.
Galilean transformation.
One-dimensional, steady solutions.
Steady shock jumps.
Ordinary di?erential equations of motion.
Conservative form.
Unreduced non-conservative form.
Reduced non-conservative form.
Rankine-Hugoniot analysis.
Rayleigh line.
Hugoniot curve.
Shock solutions.
Equilibrium solutions.
Chapman-Jouguet solutions.
Weak and strong solutions.
Summary of solution properties.
ZND solutions: One-step irreversible kinetics.
CJ ZND structures.
Strong ZND structures.
Weak ZND structures.
Piston problem.
Detonation structure: Two-step irreversible kinetics.
Strong structures.
D ? D.
D = D.
Weak, eigenvalue structures.
Piston problem.
Detonation structure: Detailed H2 ? O2 ? N2 kinetics.
Blast waves.
Goveing equations.
Similarity transformation.
ndependent variables.
Dependent variables.
Derivative transformations.
Transformed equations.
Mass.
Linear momentum.
Energy.
Dimensionless equations.
Mass.
Linear momentum.
Energy.
Reduction to non-autonomous form.
Numerical solution.
Calculation of total energy.
Comparison with experimental data.
Contrast with acoustic limit.
Bibliography.